fix: address all known follow-up issues except NetEase batch precheck

Surface failures + tighten edges:

1. Toast for /play-song & /play-playlist failures. Backend now returns
   {ok, message} (localized in Chinese to match the rest of the UI).
   Store stashes a notification on ok=false; new Toast.vue mounted in
   App.vue shows it for 3-5s then fades. Clicking the X dismisses
   immediately. Sits above the player on desktop and above the mobile
   tabbar on phones.

2. QQ collected playlists pagination. fcg_get_profile_order_asset.fcg
   returns max 30 per call; we now loop using has_more / short-page
   detection up to a 300-playlist hard cap. Single-call users (typical)
   exit the loop on the first iteration so no extra requests.

3. getPlayableSongIds chunking. 100 mids per request keeps URL well
   under 8KB; chunk-level errors are isolated so a transient blip on
   one chunk doesn't poison the whole batch. Returns null only when
   every chunk failed (caller falls back to sequential retry).

4. SourceTabs single-source mode now renders a small subdued "网易云"
   or "QQ" label instead of vanishing entirely, so the user always
   knows which platform's data they're looking at.

5. Hide the "我的歌单 N" count badge when N=0 — Home and Library no
   longer show "我的歌单 0" with an empty grid.

6. Auth state change invalidates fetchHomeData cache. Previously, a
   user who logged out as account A and into account B within 5
   minutes would see A's playlists. Now we always re-check auth at
   the top of fetchHomeData and bypass the TTL cache when authStatus
   has changed.

Out of scope:
- NetEase analogous batch precheck (per request).
- 60s TS3 UDP idle disconnect — that's the bundled @honeybbq/teamspeak-
  client UDP layer kicking when no server packet arrives in 60s. It's
  baked in (constant `v=6e4`) and not exposed as an option, and root
  cause is server-side or network-layer behavior we can't reach from
  here.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

web/src/views/Home.vue

@@ -76,7 +76,7 @@
     <section class="section" v-if="userAvailable.length > 0">
       <h2 class="section-title">
         我的歌单
-        <span class="section-count">{{ currentUserPlaylists.length }}</span>
+        <span v-if="currentUserPlaylists.length > 0" class="section-count">{{ currentUserPlaylists.length }}</span>
         <SourceTabs v-model="userSource" :sources="userAvailable" />
       </h2>
       <div class="playlist-grid">